Internal Pressure Standard Research Articles

The development of internal pressure standards for in-house elastic wave velocity measurements in multi-anvil presses.

Ultrasonic systems are powerful tools to determine elastic wave velocities of minerals and materials at high pressure and temperature and have been extensively developed in recent decades. However, accurate measurement of sample length is required to convert travel times into wave velocities, limiting their use to synchrotron facilities or room temperature experiments in laboratories. We have made use of a close collaboration between the Bayerisches Geoinstiut and the P61B end-station beamline (PETRA III - DESY) to install ultrasonic systems and develop a novel dual travel time method for in situ pressure determination without the need for synchrotron radiation. Our method relies on the travel times of elastic waves through a reference material; it requires a thermocouple and is non-intrusive, with the reference material replacing the backing plate of the high-pressure assembly. Pressures obtained from this dual travel time method show excellent agreement with those obtained from x-ray diffraction using synchrotron radiation on standard materials. Our novel method enables in situ pressure determination at varying temperatures during in-house ultrasonic interferometry experiments. This allows us not only to determine the elastic behavior of minerals and materials but also to investigate phase diagrams, solidus, or liquidus conditions at varying pressures and temperatures during in-house experiments. During the installation of the pulse-echo ultrasonic system, we identified critical parameters for obtaining reliable data. While these requirements are well-known to experts, this study presents a comprehensive review of the different characteristics of ultrasonic systems, providing user-friendly guidelines for new users installing and operating such systems in high-pressure and high-temperature conditions.

Experimental and Computational Studies of Compression and Deformation Behavior of Hafnium Diboride to 208 GPa.

The compression behavior of the hexagonal AlB2 phase of Hafnium Diboride (HfB2) was studied in a diamond anvil cell to a pressure of 208 GPa by axial X-ray diffraction employing platinum as an internal pressure standard. The deformation behavior of HfB2 was studied by radial X-ray diffraction technique to 50 GPa, which allows for measurement of maximum differential stress or compressive yield strength at high pressures. The hydrostatic compression curve deduced from radial X-ray diffraction measurements yielded an ambient-pressure volume V0 = 29.73 Å3/atom and a bulk modulus K0 = 282 GPa. Density functional theory calculations showed ambient-pressure volume V0 = 29.84 Å3/atom and bulk modulus K0 = 262 GPa, which are in good agreement with the hydrostatic experimental values. The measured compressive yield strength approaches 3% of the shear modulus at a pressure of 50 GPa. The theoretical strain-stress calculation shows a maximum shear stress τmax~39 GPa along the (1−10) [110] direction of the hexagonal lattice of HfB2, which thereby can be an incompressible high strength material for extreme-environment applications.

High pressure structural phase transitions in Dysprosium to 202 GPa

ABSTRACT High pressure structural phase transitions in heavy lanthanide metal Dysprosium (Dy) have been studied to 202 GPa (Volume Compression ) in a diamond anvil cell employing copper as an internal x-ray pressure standard. The previously assigned monoclinic (C2/m) phase above 72 GPa has been reexamined and assigned to an orthorhombic phase with sixteen atoms per cell (oF16) based on structural refinements. The equation of state is presented to 202 GPa and indicates a volume change of 2.3% during the structural phase transition from distorted face-centered cubic (hR24) phase to oF16 phase at 72 GPa. The oF16 phase can be regarded as a pseudo-orthorhombic eight-layered structure with (b/c) ratio decreasing from an ideal value of with increasing pressure to 202 GPa. The ultrahigh pressure structural phases of Dy are compared with other members of the lanthanide series.

Theoretical and experimental studies of compression and shear deformation behavior of Osmium to 280 GPa

The compression behavior of osmium metal was investigated up to 280 GPa (volume compression V/Vo = 0.725) under nonhydrostatic conditions at ambient temperature using angle dispersive axial x-ray diffraction (A-XRD) with a diamond anvil cell (DAC). In addition, shear strength of osmium was measured to 170 GPa using radial x-ray diffraction (R-XRD) technique in DAC. Both diffraction techniques in DAC employed platinum as an internal pressure standard. Density functional theory (DFT) calculations were also performed, and the computed lattice parameters and volumes under compression are in good agreement with the experiments. DFT predicts a monotonous increase in axial ratio (c/a) with pressure and the structural anomalies of less than 1% in (c/a) ratio reported below 150 GPa were not reproduced in theoretical calculations and hydrostatic measurements. The measured value of shear strength of osmium () approaches a limiting value of 6 GPa above a pressure of 50 GPa in contrast to theoretical predictions of 24 GPa and is likely due to imperfections in polycrystalline samples. DFT calculations also enable the studies of shear and tensile deformations. The theoretical ideal shear stress is found along the (001)[1–10] shear direction with the maximal shear stress ∼24 GPa at critical strain ∼0.13.

Shear strength measurements and hydrostatic compression of rhenium diboride under high pressures

Shear strength measurements have been carried out on rhenium diboride, ReB2, to a pressure of 74 GPa using a Radial X-ray Diffraction (R-XRD) technique in a diamond anvil cell using platinum as an internal x-ray pressure standard. The R-XRD result has provided a unique insight into the deformation of hexagonal crystal lattice under non-hydrostatic compression and variation of shear strength with increasing pressure. From R-XRD data, we have estimated hydrostatic component of compression to determine an equation of state of rhenium diboride yielding a bulk modulus of K0 = 366 ± 25 GPa with a pressure derivative K0′ = 4.3 ± 0.5 in good agreement with hydrostatic density functional theory calculations. The average lower bound of shear strength (τ) from various diffraction planes was then calculated using the measured interplanar d-spacing (dm) and hydrostatic component of d-spacing (dp) to be shown to approach 6.7 ± 0.4 GPa at 70 GPa. Our results show that the anisotropic compression effects observed in ReB2 under hydrostatic compression are correlated to electronic structure changes under compression as predicted by theoretical calculations.

Ultrahigh pressure equation of state of tantalum to 310 GPa

ABSTRACTThe isothermal compression of transition metal tantalum (Ta) was studied in a diamond anvil cell by X-ray diffraction utilizing rhenium (Re) and gold (Au) as internal X-ray pressure standards. The Re pressure marker was employed during non-hydrostatic compression to pressures up to 310 GPa while the Au pressure marker was used during quasi-hydrostatic compression in a neon pressure-transmitting medium to 80 GPa. Two ultra-high pressure experiments were conducted on Ta and Re mixtures utilizing focused-ion beam machined toroidal diamond anvils with central flats varying from 8 microns to 16 microns in diameter. The Ta metal was observed to be stable in the body-centered-cubic phase to a volume compression V/V0 = 0.581. The measured equations of state (EOS) of Ta using two different calibrations of the Re pressure marker are compared with the ambient temperature isotherm derived from shock compression data. We provide a detailed analysis of EOS fit parameters for Ta under quasi-hydrostatic and non-hydrostatic conditions.

Compressive behaviors of bcc bismuth up to 55 GPa

AbstractBismuth was compressed hydrostatically and nonhydrostatically up to 55 GPa in a diamond anvil cell. The strength of bcc bismuth was determined by the radial X‐ray diffraction (RXRD) technique: Y = −0.20(5) + 0.009(1)P, which is much smaller than that of normal pressure‐transmitting media (PTM), such as NaCl, Ar, and He. Different PTM [silicone oil (SO), Ar, and He] were used to determine the hydrostatical equation of state of bcc bismuth. The determined results are consistent with each other when different PTM were used, even when no PTM was used. The typical bulk modulus and its pressure derivation of bcc bismuth are 42.7(6) GPa and 5.3(1), respectively. The differential strain introduced by nonhydrostatic stress was derived from Hooke's law and lattice strain theory (LST). The differential strain in bismuth is very small even when no PTM was used. Because of the simple, stable structure and small strength, bcc bismuth is an ideal candidate for an internal pressure standard.

Compression of bulk metallic glass Zr57Cu15.4Ni12.6Al10Nb5 to 122 GPa

Ultra high pressure X-ray diffraction studies have been carried out on group IV transition metals-based bulk metallic glass (BMG) Zr57Cu15.4Ni12.6Al10Nb5 to a pressure of 122 GPa at ambient temperature in a diamond anvil cell. Image plate X-ray diffraction studies under high pressure were carried out at a synchrotron source and the two BMG diffraction bands can be followed to the highest pressure using an internal copper pressure standard. Our experiments show that the BMG is stable to compression as high as 40% and thermal activation is needed to nucleate nanostructures/crystallization under extreme conditions. The fit to the Birch–Murnaghan equation of state gives bulk modulus (B 0)=116 GPa and its pressure derivative B′=3.04. The measured differential radial distribution function shows gradual compression of the shell structures in the BMG to extreme compressions.

Structural stability and compressibility of group IV transition metals-based bulk metallic glasses under high pressure

High-pressure x-ray diffraction studies have been carried out on the two group IV transition metals-based bulk metallic glasses (BMGs) Zr57Cu15.4Ni12.6Al10Nb5 and Ti42Zr24Cu15.5Ni14.5Be4 to a pressure of 30 GPa at ambient temperature in a diamond anvil cell. Image plate x-ray diffraction studies under high pressure were carried out at a synchrotron source and the two BMG diffraction bands can be followed to the highest pressure using an internal copper pressure standard. The amorphous phase is observed to be stable to the highest static pressure of 30 GPa suggesting that the phase change observed in dynamical pressure experiments is related to an increase in temperature. The measured bulk modulus (B0) and its pressure derivative (B′) are 118 GPa and 3.11 for Zr-based BMG and 116 GPa and 2.84 for Ti-based BMG. The measured bulk modulus for BMG’s by x-ray diffraction technique is consistent with the ultrasonic measurements. The decompression data reveal an increase in density by 3%–4% at ambient condition after pressure cycling to 30 GPa indicating reduction in excess free volume.

Determination of post‐perovskite phase transition boundary in MgSiO3 using Au and MgO pressure standards

We have determined the post‐perovskite phase transition boundary in MgSiO3 by in‐situ X‐ray diffraction measurements, using Au and MgO as internal pressure standards. Results demonstrate that phase transition occurs at 113 GPa and 2400 K with a positive Clapeyron slope of +4.7 MPa/K, based on the Au pressure scale. On the other hand, the simultaneous measurements of MgO standard show that the phase boundary is located at 119 GPa and 2400 K with a Clapeyron slope of +11.5 MPa/K, consistently with the previous experimental results based on the Pt scale and the theoretical calculations. Our experiments also indicate that the stabilities of perovskite and post‐perovskite in all of (Mg0.89Fe0.11)2SiO4, natural pyrolitic mantle, and MORB compositions are consistent with the phase transition boundary in pure MgSiO3, when all the data are compared using the same Au scale. The compositional variations in natural systems have little effect on the post‐perovskite phase transition.

New Cubic Phase ofLi3N: Stability of theN3−Ion to 200 GPa

Diamond-anvil cell experiments augmented by first-principles calculations have found a remarkable stability of the ${\mathrm{N}}^{3\ensuremath{-}}$ ion in ${\mathrm{Li}}_{3}\mathrm{N}$ to a sixfold volume reduction. A new ($\ensuremath{\gamma}$) phase is discovered above $40(\ifmmode\pm\else\textpm\fi{}5)\text{ }\text{ }\mathrm{GPa}$, with an 8% volume collapse and a band gap quadrupling at the transition determined by synchrotron x-ray diffraction and inelastic x-ray scattering. $\ensuremath{\gamma}\mathrm{\text{\ensuremath{-}}}{\mathrm{Li}}_{3}\mathrm{N}$ ($Fm3m$, ${\mathrm{Li}}_{3}\mathrm{Bi}$-like structure) remains stable up to 200 GPa, and calculations do not predict metallization until $\ensuremath{\sim}8\text{ }\text{ }\mathrm{TPa}$. The high structural stability, wide band gap, and simple electronic structure make this ${\mathrm{N}}^{3\ensuremath{-}}$ based system analogous to lower valency compounds (MgO, NaCl, Ne), meriting its use as an internal pressure standard.

Stability of phase A in antigorite (serpentine) composition determined by in situ X-ray pressure observations

Here, we precisely determined the low-pressure stability limit of phase A in the Mg-end-member antigorite bulk composition defined as the reaction forsterite + water = phase A + enstatite (“water-line” or “water-storage line”) in a multi-anvil apparatus. Pressures were determined by in situ synchrotron X-ray diffraction measurements using NaCl as an internal pressure standard. Results demonstrate that the water-line is located at 800 °C and 8.5 GPa and at 550 °C and 5.1 GPa with a Clapeyron slope of 13.6 MPa/°C. We also examined the conditions for the formation of phase A by the decomposition of antigorite on the basis of the phase relations in the systems MgO–SiO 2–H 2O (MSH) and MgO–Al 2O 3–SiO 2–H 2O (MASH). A descending slab peridotite retains water in phase A beyond the stability of antigorite only when temperature in the slab is lower than 550 or 660 °C at 5.1 GPa (corresponding to 160 km depth), in the system MSH or MASH, respectively. The double seismic planes observed within the slabs may be caused by the dehydration reaction of antigorite or chlorite. Their merging depths, which could represent the high-pressure stability limit of antigorite or chlorite, are 160 km or deeper beneath northeast Japan, Aleutian, Kamchatka and Kuril. Water included in hydrous slab peridotite is transported into the transition zone and deeper mantle in these areas but recycled to the surface in other subduction zones.

A critical evaluation of pressure scales at high temperatures by in situ X-ray diffraction measurements

We conducted multi-anvil experiments at simultaneous high pressures and temperatures using multiple internal pressure standards including Au, Pt, MgO, W, Mo, Pd, and Ag. Extensive synchrotron X-ray diffraction data for Au, Pt, and MgO were collected at pressures up to 28 GPa and temperatures between 300 and 2173 K. We compare pressures calculated from different pressure scales and demonstrate large discrepancies in pressure determination using different pressure standards or different thermal equations of state for the same standard. The comparison allows us to quantitatively determine the differences in pressure using different pressure scales in the high P – T experiments. Using the MgO scale of [J. Geophys. Res. 106 (2001) 515] as a reference pressure scale, new Au and Pt scales are presented that are consistent with the MgO scale. We further examined the validity of the assumption of constant q value (volume dependence of the Grüneisen parameter in the Mie–Grüneisen relation) for the calculations of thermal pressures, and show that an expression of q as a function of temperature and pressure may be necessary to best fit the simultaneous high P – T data.

A critical evaluation of pressure scales at high temperatures by in situ X-ray diffraction measurements

We conducted multi-anvil experiments at simultaneous high pressures and temperatures using multiple internal pressure standards including Au, Pt, MgO, W, Mo, Pd, and Ag. Extensive synchrotron X-ray diffraction data for Au, Pt, and MgO were collected at pressures up to 28 GPa and temperatures between 300 and 2173 K. We compare pressures calculated from different pressure scales and demonstrate large discrepancies in pressure determination using different pressure standards or different thermal equations of state for the same standard. The comparison allows us to quantitatively determine the differences in pressure using different pressure scales in the high P– T experiments. Using the MgO scale of [J. Geophys. Res. 106 (2001) 515] as a reference pressure scale, new Au and Pt scales are presented that are consistent with the MgO scale. We further examined the validity of the assumption of constant q value (volume dependence of the Grüneisen parameter in the Mie–Grüneisen relation) for the calculations of thermal pressures, and show that an expression of q as a function of temperature and pressure may be necessary to best fit the simultaneous high P– T data.

Experimentally determined postspinel transformation boundary in Mg2SiO4 using MgO as an internal pressure standard and its geophysical implications

We have determined the postspinel transformation boundary in Mg2SiO4 by combining quench technique with in situ pressure measurements, using multiple internal pressure standards including Au, MgO, and Pt. The experimentally determined boundary is in general agreement with previous in situ measurements in which the Au scale of Anderson et al. [1989] was used to calculate pressure: Using this pressure scale, it occurs at significantly lower pressures compared to that corresponding to the 660‐km seismic discontinuity. In this study, we also report new experimental data on the transformation boundary determined using MgO as an internal standard. The results show that the transition boundary is located at pressures close to the 660‐km discontinuity using the MgO pressure scale of Speziale et al. [2001] and can be represented by a linear equation, P(GPa) = 25.12 − 0.0013T(°C). The Clapeyron slope for the postspinel transition boundary is precisely determined and is significantly less negative than previous estimates. Our results, based on the MgO pressure scale, support the conventional hypothesis that the postspinel transformation is responsible for the observed 660‐km seismic discontinuity.

The equation of state of Bi and cross-checking of Au and Pt scales to megabarpressure

By means of x-ray diffraction experiments using a synchrotron radiationsource, the equation of state (EOS) of body-centred cubic Bi has beeninvestigated over a range of multimegabar pressure up to 222 GPa on thebasis of the Pt pressure scale and it is proposed as an internal pressurestandard over a range of megabar pressures. Pressure scales of the EOS of Auand Pt were cross-checked and the accuracy of the scales is discussed.

Equation of state of gold and its application to the phase boundaries near 660 km depth in Earth’s mantle

The pressure–volume–temperature equation of state (EOS) of gold is fundamental to high-pressure science because of its widespread use as an internal pressure standard. In particular, the EOS of gold has been used in recent in situ multi-anvil press studies for determination of phase boundaries related to the 660-km seismic discontinuity. These studies show that the boundaries are lower by 2 GPa than expected from the depth of the 660-km discontinuity. Here we report a new P–V–T EOS of gold based on the inversion of quasi-hydrostatic compression and shock wave data using the Mie–Grüneisen relation and the Birch–Murnaghan–Debye equation. The previously poorly constrained pressure derivative of isothermal bulk modulus and the volume dependence of Grüneisen parameter ( q=d ln γ/d ln V) are determined by including both phonon and electron effects implicitly: K′ 0 T =5.0±0.2 and q=1.0±0.1. This combined with other accurately measured parameters enables us to calculate pressure at a given volume and temperature. At 660-km depth conditions, this new EOS yields 1.0±0.2 GPa higher pressure than Anderson et al.’s EOS which has been used in the multi-anvil experiments. However, after the correction, there still exists a 1.5-GPa discrepancy between the post-spinel boundary measured by multi-anvil studies and the 660-km discontinuity. Other potential error sources, such as thermocouple emf dependence on pressure or systematic errors in spectroradiometry, should be investigated. Theoretical and experimental studies to better understand electronic and anharmonic effects in gold at high P–T are also needed.

In situ measurements of the majorite‐akimotoite‐perovskite phase transition boundaries in MgSiO3

Here we report the phase boundaries between majorite, akimotoite (ilmenite), and perovskite in MgSiO3 determined by in situ measurements in a multi‐anvil apparatus. We used both gold and platinum as internal pressure standards at high pressure and temperature. Our results obtained at 1400‐2000°C, together with previous results obtained at 1000‐1200°C by Ono et al. [2001], precisely locate the akimotoite‐perovskite transition boundary at P (GPa) = 25.09 ‐ 0.0027 × T (°C), based on the P‐V‐T equation of state of gold [Anderson et al., 1989]. Our new experimental data show the position of triple point to be 20.0 GPa and 1920°C. The present measurements reconfirm our earlier study [Hirose et al., 2001] that Anderson's gold pressure scale gives slightly higher pressures than the platinum pressure scale proposed either by Jamieson et al. [1982] or Holmes et al. [1989].

Thermal decomposition of rhombohedral KClO3from 29–76 kilobars and implications for the molar volume of fluid oxygen at high pressures

KClO 3 thermal decomposition has been studied from 29–76 kilobars using a multianvil high-pressure device and in-situ energy-dispersive X-ray diffraction and off-line quenching experiments. The rhombohedral form of KClO 3 was found to decompose to the B2 form of KCl and O 2 via an orthorhombic KClO 4 intermediate over this pressure interval. The decomposition temperature was found to vary only slightly with pressure. The online experiments gave decomposition temperatures between 500 and 580 °C. Further off-line quenching experiments using sealed gold tubes determined the equilibrium decomposition boundary to be 550 ± 15 °C over this pressure range. Unit-cell parameters and volumes were determined for the high-pressure phases of KClO 3 and KCl from the diffraction data. The partial molar volume of O 2 was calculated from the difference in the solid volumes. Oxygen fluid volumes were then calculated along the decomposition boundary and vary from 10.6 ± 0.2 cm 3 /mol at 29 kbar to 9.6 ± 0.1 cm 3 /mol at 76 kbar. These volumes are 30 to 50% less than previous estimates determined from shock wave data, and imply that oxygen can be more easily stored in Earth’s mantle and core than previously believed. The thermal equation of state of the B2 form of KCl was investigated online using NaCl as an internal pressure standard. KCl was then used as an internal pressure calibrant for the online KClO 3 decomposition experiments. The mechanical behavior of the multianvil high-pressure device was also studied and load vs. force characteristics are presented here.

α-uranium phase in compressed neodymium metal

The light rare-earth metal, neodymium, has been studied up to 155 GPa in a diamond-anvil cell using energy dispersive x-ray diffraction with a synchrotron source. The pressures were calibrated using copper as an internal x-ray pressure standard. A phase transformation from a monoclinic phase $(C2/m,$ $4\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}/\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{l})$ to an orthorhombic \ensuremath{\alpha}-U phase $(Cmcm,4\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{s}/\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{l})$ was observed at 113\ifmmode\pm\else\textpm\fi{}6 GPa without any observable volume collapse. The observation of \ensuremath{\alpha}-U phase in Nd and, previously, in cerium and praseodymium clearly establishes this phase in light rare-earth metals. Our equation of state measurements suggest that delocalization of the f shell in Nd occurs without any volume collapse unlike Ce and Pr.